Field of the Invention
The present invention relates to an apparatus and method for electrical properties tomography and, more particularly, to an apparatus and method for imaging electrical properties of brain tissues including conductivity and permittivity using magnetic resonance imaging (MRI) signals.
Description of the Related Art
Techniques for measuring electrical properties of human tissues are broadly divided into Electrical Impedance Tomography (EIT) and Magnetic Resonance Imaging (MRI).
In EIT, a plurality of electrodes is attached to a human body, and electric potential produced when an alternating current is applied to the human body is measured. Then, an image of conductivity distribution in the human body is obtained from the measured electric potential information using an inverse problem solver.
However, for EIT, the resolution of images is very low, and multiple electrodes need to be attached to the epidermis of the human body. For this reason, EIT is not widely used clinically.
With MRI, both the conductivity image and permittivity image of the human body may be obtained. To obtain an MRI image, a radiofrequency magnetic field pulse having the operation frequency of MRI as the center frequency needs to be applied to the human body. The radiofrequency magnetic field pulse changes the hydrogen nucleus to a higher energy level, and the hydrogen atom in a high energy level may trigger a radiofrequency electric potential signal in the radiofrequency coil installed around the human body. The electric potential signal induced in the radiofrequency coil is typically referred to as an MRI signal. An MRI image is obtained from this image signal.
However, since the radiofrequency magnetic field pulse has characteristics of an electromagnetic wave, the wavelength of the electromagnetic wave is greatly shortened within the human body which contains water molecules having high permittivity, and it is difficult to obtain MRI images of a good quality.
Accordingly, the conventional technology for measuring electrical properties of human tissues acquires an image of distribution of B1 through B1 mapping, which is a technique for imaging the magnitude and phase distribution of a radiofrequency magnetic field formed in the human body with MRI, and then uses Magnetic Resonance-Electrical Properties Tomography (MR-EPT) to obtain a conductivity image and a permittivity image from the image of distribution of B1.
With conventional MR-EPT, conductivity and relative permittivity may be calculated from the distribution image of B1 for a region in which uniform conductivity and permittivity are provided, through an inverse problem solver using Equations 1 and 2 given below.
                    σ        =                              1            μω                    ⁢          Im          ⁢                      {                                                            ∇                  2                                ⁢                                  B                  1                                                            B                1                                      }                                              Equation        ⁢                                  ⁢        1            
Herein, σ denotes conductivity, μ denotes the permeability of a radiofrequency magnetic field, and ω denotes an operation frequency of MRI.
                              ɛ          r                =                              -                          1                                                μɛ                  0                                ⁢                                  ω                  2                                                              ⁢          Re          ⁢                      {                                                            ∇                  2                                ⁢                                  B                  1                                                            B                1                                      }                                              Equation        ⁢                                  ⁢        2            
Herein, ε0 is the free space permittivity and εr denotes relative permittivity.
However, with the MR-EPT technique, Equation 1 for acquiring conductivity and Equation 2 for acquiring permittivity cannot be established in a region in which conductivity and permittivity are not uniform, namely a boundary region where different tissues are adjacent to each other, and thus images of electrical properties obtained from Equation 1 and Equation 2 may have a significant error.
Further, Equations 1 and 2 employ Laplacian (∇2), which is a second order derivative, to obtain conductivity and permittivity, but the Laplacian operation tends to significantly amplify noise in performing image measurement. Accordingly, if a B1 distribution image contains noise or has a measurement error, the conductivity image and permittivity image obtained through Equations 1 and 2 may have a significant error.
Moreover, the B1 distribution image contains lots of noise compared to a hydrogen density image, which is a typical MRI image. Accordingly, the conductivity image and permittivity image acquired from the B1 distribution image are typically severely damaged by noise, and thus MR-EPT cannot be used for clinical diagnosis.
Alternatively, in a technology to acquire images of electrical properties of tissue without using the conventional differential calculation, the water content of tissue is acquired using the density of hydrogen atoms, spin-lattice relaxation time T1 and spin-spin relaxation time T2, which are typical physical quantities presented by MRI imaging of the tissue, and a conductivity image and permittivity image are acquired from the acquired water content.
The conventional technology has yielded the Equation 3 below based on the relation between the spin-lattice relaxation time and the water content, which are in close connection with diffusivity of water molecules in a tissue.
                    W        =                  1                      A            +                          B              /                              T                1                                                                        Equation        ⁢                                  ⁢        3            
Herein, A and B are constants, which may vary with strength of a main magnetic field of MRI.
                              I          r                =                                            I              s                                      I              l                                =                      κ            ⁢                                          1                -                                  2                  ⁢                                      e                                                                  -                                                  (                                                                                    TR                              s                                                        -                                                          TE                              /                              2                                                                                )                                                                    /                                              T                        1                                                                                            +                                  e                                                            -                                              TR                        s                                                              /                                          T                      1                                                                                                  1                -                                  2                  ⁢                                      e                                                                  -                                                  (                                                                                    TR                              l                                                        -                                                          TE                              /                              2                                                                                )                                                                    /                                              T                        1                                                                                            +                                  e                                                            -                                              TR                        l                                                              /                                          T                      1                                                                                                                              Equation        ⁢                                  ⁢        4            
Herein, Ir denotes a ratio for MRI signals, Is denotes an MRI image signal according to a short repetition time, I1 denotes an MRI image signal according to a long repetition time, TRs denotes a short repetition time, TR1 denotes a long repetition time, and κ denotes a correction constant.
In the conventional technology, Equation 4 below is produced using MRI image signals acquired from two different repetition times TR, which are imaging variables most widely used in MRI, and an echo time TE, and water content in the tissue is acquired using Equations 3 and 4 as simultaneous equations.
In addition, in the conventional technology, conductivity and permittivity of the tissue is estimated from Equations 5 and 6 given below, using the water content in the tissue acquired from Equation 3 and Equation 4.
                    σ        =                              σ            w                    ⁢                      W                          1              +                                                (                                      1                    -                    W                                    )                                /                2                                                                        Equation        ⁢                                  ⁢        5            
Herein, σw denotes conductivity of an ionic solution.
                              ɛ          r                =                              ɛ            w                    ⁢                                                    3                ⁢                                  ɛ                  p                                            +                              2                ⁢                                  W                  ⁡                                      (                                                                  ɛ                        w                                            -                                              ɛ                        p                                                              )                                                                                                      4                ⁢                                  ɛ                  w                                            -                              ɛ                p                            +                              2                ⁢                                  W                  ⁡                                      (                                                                  ɛ                        p                                            -                                              ɛ                        w                                                              )                                                                                                          Equation        ⁢                                  ⁢        6            
Herein, εw denotes permittivity of an ionic solution, and εp denotes permittivity of foreign particles.
In the conventional technology, however, it is difficult to analytically solve Equations 5 and 6 because they are non-linear equations. To solve Equations 5 and 6, permittivity of foreign particles needs to be obtained. However, it is substantially impossible to obtain the permittivity of foreign particles in the tissue because cell structures and protein which operate as foreign substances in the tissue come in different sizes and have different constituents.
Further, in the conventional technology, since conductivity and permittivity are calculated by putting the water content acquired from Equation 3 in Equations 5 and 6, an error of estimation of the water content may directly affect calculation of conductivity and permittivity.
As a conventional technology using water content, European Patent Application Publication No. 851,236 discloses a multi echo imaging technique for estimating the water content. According to this technique, an image at the echo time equal to 0 is acquired through extrapolation based on multiple images according to multiple echo times, and the acquired image is used as an image of water content.
However, the image of water content disclosed in the aforementioned document is very vulnerable to main magnetic field inhomogeneity and radiofrequency field inhomogeneity. Accordingly, it is difficult to clinically utilize the image.